TY - JOUR
T1 - Unitarily invariant metrics on the grassmann space
AU - Qiu, Li
AU - Zhang, Yanxia
AU - Li, Chi Kwong
PY - 2006
Y1 - 2006
N2 - Let G m,n be the Grassmann space of m-dimensional subspaces of double-struck F sign n. Denote by θ 1(X,y), . . . ,θ m(X,y) the canonical angles between subspaces X,y ∈ G m,n. It is shown that ψ(θ 1(X,y), . . . ,θ m(X,y)) defines a unitarily invariant metric on G m,n for every symmetric gauge function ψ. This provides a wide class of new metrics on G m,n. Some related results on perturbation and approximation of subspaces in G m,n, as well as the canonical angles between them, are also discussed. Furthermore, the equality cases of the triangle inequalities for several unitarily invariant metrics are analyzed.
AB - Let G m,n be the Grassmann space of m-dimensional subspaces of double-struck F sign n. Denote by θ 1(X,y), . . . ,θ m(X,y) the canonical angles between subspaces X,y ∈ G m,n. It is shown that ψ(θ 1(X,y), . . . ,θ m(X,y)) defines a unitarily invariant metric on G m,n for every symmetric gauge function ψ. This provides a wide class of new metrics on G m,n. Some related results on perturbation and approximation of subspaces in G m,n, as well as the canonical angles between them, are also discussed. Furthermore, the equality cases of the triangle inequalities for several unitarily invariant metrics are analyzed.
KW - Canonical angles
KW - Perturbation
KW - Singular values
KW - Subspace
KW - Unitarily invariant metric
UR - https://www.scopus.com/pages/publications/33646271585
U2 - 10.1137/040607605
DO - 10.1137/040607605
M3 - Article
AN - SCOPUS:33646271585
SN - 0895-4798
VL - 27
SP - 507
EP - 531
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
IS - 2
ER -